Using a 44T big chainring and an 11xXX cassette will give you a 108 gear-inch high gear which is identical to a 52x13 so that should be more than adequate unless you insist on pedaling down big hills.
You will also have a very low low gear either 22x32 (18.5 gear-inches) or 22x34 (17.4 gear-inches)depending on the cassette you choose which should get you up anything!
Summary, XTR will cover about any conditions you are likely to face.
The Grand Canyon area is at 7500' at the South Rim and about 8500' at the North rim so the altitude makes it feel harder. And, while the climbs aren't real steep, they can be very long.